Re: Best secondary size

["Tesla list" <tesla-at-pupman-dot-com>]

Original poster: "Dr. Resonance" <resonance-at-jvlnet-dot-com> 


I agree with your assessment.  I was essentially using the k value as a
coeff. of efficiency which multiplied times the Vin x sqr Ls/Lp would give a
value for approx. output.

It could also be incorporated, as you correctly pointed out, in other
equations related to the Fs and Fp values, ie, Fsec = Fpri.

Dr. Resonance

 >
 > You and Malcolm are right. I get the feeling sometimes coupling and
efficiency are being
 > confused in these discussions.
 >
 > The coupling between prim. and sec. coil, k,  is defined by
 >
 >             k = M/SQRT(Lp*Ls)                    (1)
 >
 > M being the mutual inductance of prim. and sec. coil.
 >
 > The efficiency, eps, of the system expresses how much of the primary
 > energy (e.g. in C1) will *eventually* end up in C2:
 >
 >             Es = eps*Ep                          (2)
 >
 > There is not really a direct link between k and eps, but there *is* a
 > link between how many oscillations it takes to transfer the total
 > primary energy, Ep, to C2 and k. The smaller k, the longer it takes
 > for Ep to end up at C2.
 > In [1] the following approximate expression is given for this transfer
 > time tau
 >
 >             tau = (1/(2*f_res))*SQRT(1-k^2)/k    (3)
 >
 > so if k = 0.15 -> tau = (1/(2*f_res))*6.6
 >     if k = 0.3  -> tau = (1/(2*f_res))*3.2
 >
 > in case k = 0.15 it takes 6.6 half oscillations for Ep to arrive at C2;
 > in the ideal case then the spark gap will quench, so the energy
 > stays in the secundary circuit and will exponentially decay.
 >
 > Since Ep = 0.5*Cp*Vp^2, and the same for Es, one gets from (2)
 >
 >             Vs = Vp*SQRT(eps*Cp/Cs)              (4)
 >
 > or, expressed in inductances,
 >
 >             Vs = Vp*SQRT(eps*Ls/Lp)              (5)
 >
 > k does not occur in (4) and (5)
 >
 > ------------------
 > [1] - Kenneth D. Skeldon, Alastair I. Grant and Slan A. Scott, "A high
 > potential
 >        Tesla coil impulse generator for lecture demonstrations and science
 > exhibitions",
 >        Am. J. Phys. 65(8), 744-754 (1997)
 >
 >
 >
 > hope this is helpful,    Rob Maas
 >
 >
 >